Three names for one tooth size
Module, diametral pitch and circular pitch all describe how big the teeth are, and cutters get marked in whichever system the maker uses. Module is the pitch diameter in millimetres divided by the tooth count. Diametral pitch is the tooth count divided by the pitch diameter in inches, so it goes the other way and a bigger number means a smaller tooth. Circular pitch is the distance from one tooth to the next measured round the pitch circle.
0.8 module works out at 31.75 diametral pitch and 0.0989 inches of circular pitch. The selector converts whichever way you need, because the cutter in the drawer and the drawing on the bench are frequently marked in different systems.
The blank is a tip circle
Pitch diameter is a fiction: a circle you cannot put a caliper on, which is the tooth count times the module. The blank you actually turn is that plus two addendums, because the teeth stand proud of it. Ninety-six teeth at 0.8 module gives a 76.8 mm pitch diameter and a 78.4 mm blank, and the difference is 1.6 mm, one module on each side.
Turn a few thou over and skim it after cutting if you want clean tips and a true circle. Turn under and the teeth come out short at the tips with no way back.
How deep the cutter goes
Whole depth is addendum plus dedendum times the module — 1.8 mm on the defaults, which is 0.071 inches. Of that, 1.6 mm is the working depth that actually engages, and the extra 0.2 mm is bottom clearance so the tip of the mating tooth is not riding on the root of this one.
Those two factors are the fields most worth taking seriously. Clock tooth forms and machine gear forms have different proportions, and a cutter ground for one and used with the numbers for the other gives teeth that do not fit anything.
The indexing fraction
On a head with a 40 to 1 worm, cutting 96 teeth means 40 divided by 96 of a crank turn per tooth, which is five twelfths. So the hole circle has to be a multiple of twelve: 24 gives ten holes, 36 gives fifteen, 48 gives twenty. Any circle that is not a multiple of twelve simply does not land, and the page lists what would.
When nothing on your plates divides the count, the nearest circle is shown with the error per tooth in minutes of arc. That error accumulates all the way round the wheel and comes home on the last tooth, which is why a near miss is not a solution.
What it does not tell you
Nothing here says the wheel will run. Whether the cutter form matches the pinion it will drive, whether the depthing is right, whether the blank is running true, whether the count suits the train — all bench work. This page turns two numbers into the sizes you need at the lathe and stops there.
Questions people ask
How do I work out the blank diameter for a gear?
Multiply the tooth count by the module to get the pitch diameter, then add two addendums. Ninety-six teeth at 0.8 module is a 76.8 mm pitch diameter, and with a one module addendum the blank is 78.4 mm. In diametral pitch the same thing is tooth count plus two, divided by the pitch. Turn it a few thou over if you plan to skim the tips after cutting.
How deep do I cut gear teeth?
The whole depth is the addendum plus the dedendum, both expressed in modules, times the module. On the default one and one and a quarter, at 0.8 module, that is 1.8 mm or 0.071 inches. Take both factors from the tooth form data for the cutter you have, because clock forms and machine forms use different proportions.
What is the difference between module and diametral pitch?
They are reciprocals with a unit conversion. Module is pitch diameter in millimetres over tooth count, so a bigger module means a bigger tooth. Diametral pitch is tooth count over pitch diameter in inches, so a bigger number means a smaller tooth. Multiply the two together and you get 25.4: 0.8 module is 31.75 diametral pitch.
Which hole circle do I use to index 96 teeth?
With a 40 to 1 worm it is 40 over 96 of a turn per tooth, which reduces to five twelfths, so you need a circle whose hole count is a multiple of twelve. Twenty-four holes gives ten, thirty-six gives fifteen, forty-eight gives twenty. Nothing that is not a multiple of twelve will land, and the page lists which counts would.
What if no hole circle divides my tooth count?
The page says so plainly and shows the nearest circle with the error per tooth in minutes of arc, so you can see how far off it is. That error is not random — it accumulates round the blank and turns up as a wide or narrow last tooth. The alternatives are a different plate, a differential arrangement, or a tooth count you can actually divide.